Advanced Linear Models for Data Science 1: Least Squares

Advanced Linear Models for Data Science 1: Least Squares

Johns Hopkins University

About this course: Welcome to the Advanced Linear Models for Data Science Class 1: Least Squares. This class is an introduction to least squares from a linear algebraic and mathematical perspective. Before beginning the class make sure that you have the following:
- A basic understanding of linear algebra and multivariate calculus.
- A basic understanding of statistics and regression models.
- At least a little familiarity with proof based mathematics.
- Basic knowledge of the R programming language.
After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general understanding of regression models.

Who is this class for: This class is for students who already have had a class in regression modeling and are familiar with the area who would like to see a more advanced treatment of the topic.

We cover some basic matrix algebra results that we will need throughout the class. This includes some basic vector derivatives. In addition, we cover some some basic uses of matrices to create summary statistics from data. This includes calculating and subtracting means from observations (centering) as well as calculating the variance.

7 videos, 4 readings

Video: Introduction

Reading: Welcome to the class

Reading: Course textbook

Reading: Grading

Reading: In this module

Video: Matrix derivatives

Video: Coding example

Video: Centering by matrix multiplication

Video: Coding example

Video: Variance via matrix multiplication

Video: Coding example

Graded: Background Quiz

WEEK 2

One and two parameter regression

In this module, we cover the basics of regression through the origin and linear regression. Regression through the origin is an interesting case, as one can build up all of multivariate regression with it.

6 videos, 2 readings

Reading: Before you begin

Video: Regression through the origin

Video: Centering first

Video: Coding example

Reading: Before you begin

Video: Connection with linear regression

Video: Coding example

Video: Fitted values and residuals

Graded: One Parameter Regression Quiz

WEEK 3

Linear regression

In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.

8 videos, 2 readings

Reading: Before you begin

Video: Least squares

Video: Coding example

Video: Prediction

Video: Coding example

Video: Residuals

Video: Coding example

Reading: Generalizations

Video: Generalizations

Video: Generalizations example

Graded: Linear Regression Quiz

WEEK 4

General least squares

We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.

6 videos, 1 reading

Reading: Before you begin

Video: Least squares

Video: Coding example

Video: Second derivation of least squares

Video: Projections

Video: Third derivation of least squares

Video: Coding example

Graded: General Least Squares Quiz

WEEK 5

Least squares examples

Here we give some canonical examples of linear models to relate them to techniques that you may already be using.

4 videos

Video: Basic examples of design matrices and fits

Video: Group effects

Video: Change of parameterization

Video: ANCOVA

Graded: Least Squares Examples Quiz

WEEK 6

Bases and residuals

Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.

6 videos

Video: Bases, introduction

Video: Bases 2, Fourier

Video: Bases 3, SVDs

Video: Bases, coding example

Video: Introduction to residuals

Video: Partitioning variability

Graded: Bases Quiz

Graded: Residuals Quiz

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Ratings and Reviews

Rated 4.4 out of 5 of 56 ratings

A

Great Course

RB

Very helpful! Tanks!

JM

Good course. Quite hard. Linear algebra should be your second language as it is assumed to be mastered. Exams should include some personal work.

I enjoyed the math and it helped me to review my linear algebra and got new intuitions on linear regression. But there are a few typos that need to be fixed. It would be better to open a forum and let student discuss with each other.